On the Youla-Kucera parametrization for nonlinear systems

Paice, Andrew; Moore, John B.

doi:10.1016/0167-6911(90)90027-r

Cited by 59 publications

(20 citation statements)

References 5 publications

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“…Lemma 5: Suppose the controller transfer matrix K is factorized according to (19). Then K is (J µ , J µ )-unitary if and only if the parameter Q ∈ RH ∞ satisfies…”

Section: Quantum Version Of the Youla-kučera Parameterizationmentioning

confidence: 99%

“…which must be satisfied for all s ∈ C, is representable in terms of the right factorization from (19) as…”

Section: Quantum Version Of the Youla-kučera Parameterizationmentioning

confidence: 99%

“…The following lemma represents (J µ , J µ )-unitarity in terms of the Youla-Kučera parameter Q from (19).…”

Section: Quantum Version Of the Youla-kučera Parameterizationmentioning

confidence: 99%

“…The state space representation of all stabilizing controllers has also been addressed for finite-dimensional, linear timeinvariant [18] and time-varying [3] systems. Furthermore, the approach was shown to be applicable to a class of nonlinear systems [9], [19], [1]. In the present paper, we employ the stable factorization approach in order to develop a quantum counterpart of the classical Youla-Kučera parameterization for describing a set of linear coherent quantum controllers that stabilize a linear quantum system.…”

Section: Introductionmentioning

confidence: 99%

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Parameterization of stabilizing linear coherent quantum controllers

Sichani¹,

Petersen²,

Vladimirov³

2015

2015 10th Asian Control Conference (ASCC)

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This paper is concerned with application of the classical Youla-Kučera parameterization to finding a set of linear coherent quantum controllers that stabilize a linear quantum plant. The plant and controller are assumed to represent open quantum harmonic oscillators modelled by linear quantum stochastic differential equations. The interconnections between the plant and the controller are assumed to be established through quantum bosonic fields. In this framework, conditions for the stabilization of a given linear quantum plant via linear coherent quantum feedback are addressed using a stable factorization approach. The class of stabilizing quantum controllers is parameterized in the frequency domain. Also, this approach is used in order to formulate coherent quantum weighted H 2 and H ∞ control problems for linear quantum systems in the frequency domain. Finally, a projected gradient descent scheme is proposed to solve the coherent quantum weighted H 2 control problem.

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“…Lemma 5: Suppose the controller transfer matrix K is factorized according to (19). Then K is (J µ , J µ )-unitary if and only if the parameter Q ∈ RH ∞ satisfies…”

Section: Quantum Version Of the Youla-kučera Parameterizationmentioning

confidence: 99%

“…which must be satisfied for all s ∈ C, is representable in terms of the right factorization from (19) as…”

Section: Quantum Version Of the Youla-kučera Parameterizationmentioning

confidence: 99%

“…The following lemma represents (J µ , J µ )-unitarity in terms of the Youla-Kučera parameter Q from (19).…”

Section: Quantum Version Of the Youla-kučera Parameterizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parameterization of stabilizing linear coherent quantum controllers

Sichani¹,

Petersen²,

Vladimirov³

2015

2015 10th Asian Control Conference (ASCC)

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“…This was largely separate from the work on adaptive systems, though at one point the ideas came together with his development of a tool for nonlinear systems like the one he had found for linear systems with T. T. Tay and successfully applied in the F111 context. Given a physical system and an associated controller, both in general nonlinear, it became possible to characterize changes in the controller that should be introduced consequent upon changes in the underlying physical plant, in order to retain desirable performance, including fundamentally closed-loop stability [162], [163], [184].…”

Section: Later He Was Elected a Fellow Of The Australian Academy Of Tmentioning

confidence: 99%

John Barratt Moore 1941–2013

Anderson¹

2014

Hist. Rec. Aust. Sci.

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John Moore was born in Lungling, China on 3 April 1941 and died in Canberra on 19 January 2013. He was an electrical engineer who spent most of his distinguished career at the University of Newcastle and the Australian National University following industrial experience and graduate education in Silicon Valley, California. He was a Fellow of the Institute of Electrical and Electronic Engineers, the Australian Academy of Science and the Australian Academy of Technological Sciences and Engineering, achieving all honours at a comparatively early age, and was recognized principally for his contributions to the field of control systems.

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